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xkcd #2904: Physics vs. Magic
(imgs.xkcd.com)
Alt text:
'At the stroke of midnight, your brother will be hurtling sideways at an altitude of 150 meters' is a regular physics prediction about your nonmagical trebuchet, whereas 'you are cursed to build a brother-launching trebuchet' falls out of the Lagrangian.
Whenever dealing with exponential stuff i try to just focus on the formula of what is happening in the exponent. logarithms are taking that down to "normal space". E.g. exponential functions are like in a warp drive, but you still have ships that can warp faster than others.